Choose the most appropriate word from the options given below to complete the following sentence.
Q. ________ is the key to their happiness; they are satisfied with what they have.
The sentence already mentions a trait that they are satisfied with what they have thus it becomes easy for us to choose the correct word. The meanings of the words are:
Contentment → being satisfied with what one has
Ambition → a strong desire to do or achieve something.
Perseverance → persistence in doing something despite difficulty or delay in achieving success.
Hunger → a feeling of discomfort or weakness caused by lack of food, coupled with the desire to eat.
Thus, contentment is the correct answer.
Choose the most appropriate words from the options given below to fill in the blanks.
Q. She was ______ to travel abroad and _____ in the field of commerce as per her wishes.
The sentence mentions a person doing something as per her wishes thus the first word must be a positive reaction. 'Restive' which means 'restless' and 'jinxed' which means 'cursed' are incorrect here. Between options 1 and 3,the word 'elated' which means 'too happy' and the word 'venture' which means 'undertake a risky or daring journey or course of action' fit here correctly. The word 'cease' means 'stop' and does not convey a proper meaning. Thus option 3 is the correct answer.
The Headmaster ___________ to speak to you.
Which of the following options is correct to complete the above sentence?
The correct tense that fits here is simple present and the subject being singular, the verb should be in the correct form too. Thus 'wants' is the correct answer. The other options are incorrect as:
Is wanting ⇒ it is in present continuous tense which is used to denote an activity which is continuing
Want ⇒ subject is singular thus the verb cannot be in plural form
Was wanting ⇒ it is in past continuous tense which is used to denote an activity which was continuing in the past
Thus option 2 is the correct answer.
The graph shows cumulative frequency % of research scholars and the number of papers published by them. Which of the following statements is true?
In this problem, cumulative frequency is given, so converting into frequency
From the table, it is clear that option b, i.e.
60% of the scholars published at least 2 papers is correct.
If 2X + 9 = 3 then the possible value of X  X^{2} would be:
So 30 will be correct as per provided options.
A growing world population has caused growing concerns about increasing famine. The population in 2000 was 6 billion. Ten years later the population was 7 billion. There were also more people affected by famines in 2010 than in 2000. Furthermore, in each year from 2000 to 2010, when the world's population increased, so did the number of those affected by famine.
Based on the information given, which of the following is true?
The number affected by famine always increases with the population. Therefore, if the population increased in 2005, then the number of those affected by famine also increased.
If there was an increase in 2005, there must have been more people affected in that year than the previous year of 2004.
The available information does not allow us to draw any of the other inferences.
The number of those affected by famine could increase without a corresponding percentage of the population increase.
Neither can we draw inferences about any particular year between 2000 and 2010.
Note:
Option 2 cannot be correct because consider a case where in 2000 the population is 100 , and people affected are 50
in 2001 the population grew to say 200, and people affected is 100
So in Both cases the percentage of people affected is 50% but the number of people affected grew.
A tunnel of length 360 m is to be constructed. As per the plan, the team has to complete the tunnelling within a specified period of time. For the first four days, the tunnelling was done according to the plan. However, it was found that the resources were being underutilized. It was then decided that the rate of tunnelling should be increased and then they started tunnelling 15 m more than their everyday plan. Therefore, a day before the planned date they had tunnelled to a length of 380 m. How many meters of tunnelling was planned for each day?
Let, the per day tunnelling plan was ‘x’ meter and the tunnelling of 360 m was to be completed in ‘y’ day.
Therefore, xy = 360(i)
Now, as per plan tunneling was done for four days and then rate of tunnelling was increased to
(x + 15) for (y  4) days. One day before the planned date they have tunnelled 380 m.
∴ Number of days when the tunnelling was done at increased rate is
= (y – 4  1) = (y  5) days
According to the statement given the following situations can be inferred
∴ 4x + (y  5) (x + 15) = 380
⇒ 4x + xy + 15y – 5x – 75 = 380
⇒ 4x + 15y – 5x = 380 + 75 – xy
⇒ 15y – x = 380 + 75 – 360
⇒ 15y – x = 95 (ii)
Putting y value from eq (i) in eq (ii) we get
⇒ x^{2} + 95x – 5400 = 0
On solving the above quadratic equation, we get
⇒ x = 40 m
Consider a random walk on an infinite twodimensional triangular lattice, a part of which is shown in the figure below.
If the probabilities of moving to any of the nearest neighbour sites are equal. What is the probability that the walker returns to the starting position at the end of exactly three steps?
A person can take 1^{st} step in any direction independently
Suppose he moves to A
Now to return to O ( initial point) in 2 steps he can move in 2 directions. Either B or f
Thus probability he will move to either B or F will be
Suppose he moves to B
Now to return back to O
he has only 1 option
⇒ to move in BO
Probability he will move in BO direction
Total probability he will return
A paper sheet is in the shape of a right angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm^{2} then area of smaller triangle will be ______ cm^{2}.
Let PQR is the initial triangle and SQT is the final triangle.
ΔPQR is similar to ΔSQT
∵ ST = 0.75 PR
∴ SQ = 0.75 PQ
And QT = 0.75 QR
Initial Area =
Final Area =
= (0.75)^{2} × 28 = 15.75 cm^{2}
If x^{2 }+ x − 1 = 0 what is the value of
x^{2} + x – 1 = 0
x^{2} + x = 1
x(x + 1) = 1
Again squaring
Which of the following Boolean expression represents the given logic circuit?
Y = AB + A(B + C) + B(B + C)
= AB + AB + AC + BB + BC
= AB + AC + B + BC
= AB + AC + B(1 + C)
= AB + AC + B
= B(A + 1) + AC
= B + AC
When a 2300/230 V, 50 kVA, 50 Hz transformer is connected as an auto transformer to supply a 2300 V circuit form 2530 V source, the kVA rating of the auto – transformer will be _______(in kVA)
kVA rating of transformer = 50 kVA
Auto transformer rating = 2300 / 2530
kVA rating of auto transformer
Transformer connections of two three phase transformers are given in the options. Which of the pair is not suitable for the parallel operation.
For the parallel operation, phase displacement angle between secondaries of both transformers must be zero. That means both the transformers must belong to same phase group.
In the given options,
Y/Zig Zag Y and Y/Y belongs to different phasor groups. Hence this pair is not suitable for parallel operation.
An 8 pole 3ϕ induction motor has an equivalent rotor resistance of 0.07 Ω/Phase. If its stalling speed is 630 RMP, how much resistance must be added per phase to obtain maximum torque at starting? Ignore magnetizing current.
X_{2} = 0.4375 Ω
S_{starting}
R_{ext} = 0.3675 Ω
For a system to be minimum phase
The Basic difinition of minimum phase system in Zdomain is it should have all poles and zerores inside the unit circle.
H(z) stable and causal:
All poles of H(z) are inside the unit circle.
All poles of i.e. zeroes of H(z) are inside unit circle.
Let x[n] = e^{2n} u[n] be the input to a system. Which of the following impulse responses gives the bounded output for this input?
A system is said to be BIBO stable if it’s impulse response is absolutely summable,
Out of all the responses only is absolutely summable.
Is not absolutely summable it is divergent.
In a 12 phase full wave rectifier if source frequency is 30 Hz, then the ripple frequency will be_____Hz
We know that
Ripple frequency = 2nf = 2 × 12 × 30 = 720 Hz
A 3 phase bridge inverter delivers power to a resistive load 400 V DC source. For a start connected load of 10 Ω/phase. Determine load power (in watt) 120^{0} conduction mode.
The admittance locus of the circuit shown in figure is
While testing a coil having a resistance of 1 Ω, resonance occurred when the oscillator frequency was 10 MHz and the variable capacitor was set at pF. What is effective value of the coil?
The Bode plot of a system is shown in figure below the magnitude (in dB) at ω = 10 rad/sec is___________ (Assume initial low frequency is 0.5 rad/sec)
Magnitude at 10 rad/sec is same as magnitude at 2 rad/sec
6 dB/octave = 20 dB/decade
y = 24.04 dB
The frequency at which polar plot of intersects the 180^{0} phase line is ______ radian/sec
For intersection with 180^{0} axis
∠GH = 180^{0}
Power in a threephase star connected balanced inductive load is measure by two wattmeter method. The phase voltage and phase current are 200 V and 10 A, respectively. The powerfactor of load is 0.5. The readings P_{1} and P_{2} of the two wattmeter’s are
Given that,
Phase voltage (V_{ph}) = 200 V
Phase current (I_{ph}) = 10 A
Power factor = cos ϕ = 0.5
⇒ ϕ = cos^{1} (0.5) = 60^{0}
In two wattmeter method,
W_{1} = V_{L}I_{L} cos (30 + ϕ)
And
W_{2} = V_{L}I_{L} cos (30 – ϕ)
A galvanometer with a full scale current of 2 A has internal resistance of 500 Ω. The multiplying power of 20 Ω shunt with this galvanometer is –
Given that, I = 2 A
R_{m} = 500 Ω
R_{sh} = 20 Ω
We know that,
A certain 8bit DAC has a full scale output of 2mA and full scale error of ± 0.5 % full scale reading. The maximum possible output current for an input of 10000000 is__________ μA.
What is the output voltage V_{o} of the given circuit.
Voltage at A point
By using virtual short circuit condition
V_{A} = V_{B} = 8V
Apply KCL at node B
Frequency compensation is used in opamp to increase its
Frequency compensation is used in operational amplifiers to improve the stability of the opamp over the input signal frequency range.
In a short transmission line, if the impedance of the line is (0.01 + j0.15) per unit when the load current is 1.0 p.u. at 0.8 lag power factor and the receiving end voltage V_{r} = 1.0 p.u, what is the regulation of the line?
Given that, impedance = (0.01 + j 0.15) p.u.
Resistance (R) = 0.01 p.u.
Reactance (X) = 0.15 p.u.
Voltage regulation
% V.R = [R cos ϕ_{r} + X sin ϕ_{r}] × 100
= [0.01 × 0.8 + 0.15 × 0.06] × 100
= 0.098 × 100 = 9.8%
A three phase transmission line has a selfreactance of 0.2 pu and mutual reactance of 0.05 pu. The sum of positive sequence reactance, negative sequence reactance and zero sequence reactance is __ (in pu)
Given that, X_{s} = 0.2 pu
X_{m} = 0.05 pu
X_{1eq} = X_{s}  X_{m} = 0.2 – 0.05 = 0.15 pu
X_{2eq} = X_{s}  X_{m} = 0.2 – 0.05 = 0.15 pu
X_{0eq} = X_{s} + 2X _{m} = 0.2 + 2 (0.05) = 0.3 pu
X_{1eq} + X_{0eq} + X_{2eq} = 0.6 pu
In a 30 bus lower system networks, there are 3 voltage controlled buses. The size of Jacobian matrix useful for power system analysis will be
The size of Jacobian matrix = (2n  2  m) × (2n  2  m)
Where n is number of buses
M is number of voltage controlled buses
Size of Jacobian matrix = (2 (30)  2  3) × (2 (30)  2  3)
= 55 × 55
If the determinant of an n × n matrix A is zero, then
(1) If the determinant of an n × n matrix A is zero then, rank (A) ≤ n – 1.
(2) The trace of A need not be zero.
(3) From the properties of Eigen values, product of Eigen values = determinant = 0.
⇒ At least one of the Eigen values is zero
(4) x = 0 is a trivial solution of Ax = 0
Only trivial solution exists when rank of matrix (A) = n.
Here rank (A) ≤ n – 1, hence infinitely many solutions exists.
There are five students S_{1}, S_{2}, S_{3}, S_{4} and S_{5} in a class and for them there are five seats R_{1}, R_{2}, R_{3}, R_{4} and R_{5} arranged in a row, where initially the seat R_{i} is allotted to the student S_{i}, I = 1, 2, 3, 4, 5, But, on the examination day, the five students are randomly allotted the five seats.
The probability that, on the examination day, the student S_{1} gets the previously allotted seat R_{1}, and NONE of the remaining students gets the seat previously allotted to him/her is
This is the case of de arrangement
n(A) = No. of ways of deranging 4 objects
The Laplace transform of
Find the area of the region bounded by the curves (see in the graphical represented figure)
Given equations are
Intersection point of these two curves will be (1, 1)
Let consider a vertical strip as shown in the figure, then the limits will be X varies from 0.5 to 1 and y varies from
Now the area will be,
is an analytic function. If u(x, y) = 4y(1 – x), then v(x, y) will be
Find the gain margin (in db) for a system whose characteristic equation is s^{3} + 6s^{2} + 8s + 10 = 0
Characteristic equation
s^{3} + 6s^{2} + 8s + 10 = 0
Now find ω_{PC
}
Consider a space vehicle model depicted in the block diagram
A suitable compensation for this system that satisfies the specifications
a) Peak overshoot ≤ 20%
b) Velocity error constant ≥ 10 is
Objective approach
The velocity error constant is given by
Only option (a) satisfies the condition for k_{v}. Hence answer is option (a) we do not need to check for peak overshoot.
The system is defined by the state matrix . The system is
The characteristic equation of the system is obtained using
Comparing it with standard equation of 2^{nd} order system
Underdamp  system
A 3ϕ, 50 Hz Fully controlled bridge converter is Fed with 400 V AC source has Inductance 25 mH/phase. If the thyristor firing angle is 30^{0} and overlap angle is 15^{0}, the constant DC load current is ____A
If the converter shown in figure has a purely resistive load R and firing angle α = 60°, the ripple factor will be ______%.
A circuit shown in figure, the chopper feed a resistive load from a battery source. Switch S is switched at 300 kHz with duty ratio of 0.4. Find peak value of source current ripple in amp is ________A
It is boost converter
A circuit shown in the figure has a dc input voltage of 30 V, a 1 : 1 transfer and an ideal MOSFET. The inductor value is 100 μH and the switching frequency is 50 kHz. Assume that the output capacitor is large enough to hold the load voltage constant. The converter is required to deliver 4 A into a 3 Ω resistive load. The ripple current magnitude. (in A)
V_{o} = I × R_{L} = 4 × 3 = 12 V
Initially there was no energy stored in the 5 H inductor in the circuit in figure shown below when it was placed across the terminals of the voltmeter. At t = 0 the inductor was switched instantaneously to position b where it remained for 1.6s before returning instantaneously to position a. The d’Arsonval voltmeter has a full scale reading of 20 V and a sensitivity of 1000 Ω/V. What will be the reading of the voltmeter be at the instant the switch returns to position a if the inertia of the d’Arsonaval movement is negligibe?
For 0 ≤ t ≤ 1.6 s
A 3bit synchronous counter using three Dflipflops is show. The output sequence of the counter starting from Q_{0}Q_{1}Q_{2} = 000 is
Initial value of Q_{0}Q_{1}Q_{2} = 000
Sequence of the counter is: 0, 4, 6, 7, 3, 1, 0, ….
The given circuit represents the realization of a Boolean function using 8 to 1 multiplexer. The realization of the same Boolean function using 4 to 1 multiplexer will be
the output of the given multiplexer is
F = S̅_{2} S̅_{1} S̅_{0} I_{ 0} + S̅_{2} S̅_{1} S_{0} I_{ 1} + S̅_{2} S_{1} S̅_{0} I_{ 2} + S̅_{2} S_{1} S_{0} I_{ 3} + S_{2} S̅_{1} S̅_{0} I_{ 4} + S_{2} S̅_{1} S_{0} I_{ 5} + S_{2} S_{1} S̅_{0} I_{ 6} + S_{2} S_{1} S_{0} I_{7}
= A̅ B̅ C̅ I_{0} + A̅ B C̅ I_{2} + A B̅ C̅ I_{4} + ABC I_{7}
= A̅ B̅ C̅ + A̅ B C̅ + A B̅ C̅ + A B C
Now, implement the above function by using 4 to 1 MUX by taking B and C as selection lines
Now, the circuit will be
Now, implement the above function by using 4 to 1 mux by taking AB as selection lines.
Now, the circuit will be
Now implement the above function by using 4 to 1 MUX by taking A and C as selection lines
I_{0} = 1, I_{1} = 0, I_{2} = B̅, I_{3} = B
Now, the circuit will be
At 50% of full load the armature current drawn by a dc shunt motor is 40 A when connected to a 200 V supply. By decreasing the field flux its speed is raised by 20%. This also causes a 10% increase in load torque. The armature resistance including the brushes is 1 ohm. Neglecting armature reaction and saturation the percentage change in field current will be
A synchronous motor has 1000 KW, 3ϕ, Y connected 3.3 KV, 28 poles, 50 Hz. synchronous reactance of 4.20 Ω/ph. Its field excitation is adjusted to result in unity P.F operation at rated load. Compute the maximum power that the motor can deliver with its excitation remaining constant at this value.
A 3phase, 50 Hz, 12 pole induction motor has star connected rotor and the resistance measured across any two slip ring is 0.04 Ω. Its full load slip is 0.02 the torque required by the load varies as the speed squared. The torque slip curve to be a straight line. In the normal operating region. The resistance to be inserted in the rotor circuit to reduce the full load speed 350 RPM is ______
Two shunt generators A and B rated as 50 kW, 500 V and 100 kW, 500 V respectively operating in parallel deliver a total current of 250 A. The regulation of generators A and B are 6 % and 4 % respectively. The currents I_{A} and I_{B} delivered by the generators are
For generator A,
Full load current,
Full load voltage drop,
Voltage of A at load current
For generator B,
Voltage of A at load current I_{B},
If
Then the Fourier transform of the signal shown in the figure is
y(t) = x(t + 1) – x(2t  1)
A Periodic square wave is shown and defined as
The correct plot of fourier series coefficients
The Various fourier series coefficients
For the circuit shown in the figure below the value of Vo in volts is______ is
By applying KVL in the second loop,
40i_{o} – 5i_{o} + 18 i_{x} = 0
⇒ 18 i_{x} = 45 i_{o}
⇒ 2 i_{x} = 5 i_{o}
By applying KVL in the right most loop
40i_{o} + 8i_{x} + 40 = 0
⇒  40i_{o} + 4(5 i_{o}) + 40 = 0
⇒ i_{o} = 2 A
⇒ V_{o} = 40 i_{o} = 40 (2) = 80 V
For the circuit given below, find V_{AB} (in V) and R_{AB} (in Ohm)
First, open 1 kΩ branch
KCL [Super node]
For the network shown below, maximum power transferred to R_{L} is _____ (in W)
To find Thevenin’s voltage, we need to find open circuit voltage across load R_{L}.
By applying KVL at the input side.
10 + 4I_{1} + V_{1} = 0
From equations 1 and 2
⇒ V_{1} = 2V_{2} and I_{1} = V_{2}
⇒ 10 + 4V_{2} + 2V_{2} = 0
To find Thevenin’s resistance: we need to suppress all the independent source in the circuit.
V = V_{2,}
I = I_{2}.
By KVL at input loop,
Equivalent Thevenin’s network is,
Maximum power
In the circuit shown in figure the transistor has β of 200. Find the input resistance R_{in} (in Ω)
β = 200, α = 0.995
Collector (I_{c}) = α I_{E} = 0.995 × 10 = 9.95 mA
V_{c} = 9.95 × 100 = 0.995 V
Transistor working in active region
In the circuit shown below the steadystate in reached with the switch K open. Subsequently the switch is closed at time t = 0.
At time
As the steady state is reached with the switch open, at t = 0^{} the capacitor will be open and inductor will be short.
At = t = 0^{
}
At t = 0^{+}
By applying KVL
5 + I + 2I + 10 = 0
By applying kVL,
1 – V_{2} + 2 I + 10 = 0
Potential field The volume charge density at point in free space is
Two electric dipoles aligned parallel to each other and having the same axis exert a force F on each other, when a distance d apart, If the dipoles are a distance 2d a part, then the mutual force between them would be
We know that,
Force between two charges is
In 2 dipoles 4 charges present.
If distance is 2d,
⇒ F
A two generator station supplies a feeder through a bus shown in figure. Additional power is fed to the bus through a transformer from a large system which may be regarded as infinite. A reactor X is included between the transformer and the bus to limit the SC rupturing capacity of the feeder circuit breaker B to 333 MVA (fault close to breaker). Find the inductive reactance of the reactor required.
System data are:
Generator G_{1}: 25 MVA, 15% reactance
Generator G_{2}: 50 MVA, 20% reactance
Transformer T_{1}: 100 MVA, 8% reactance
Transformer T_{2}: 40 MVA, 10% reactance
Assume that all reactance are given an appropriate voltage bases. Choose a base of 100 MVA.
All reactance are given an approximate voltage bases.
Perrault no load voltage = 1 pu
Base = 100 MVA
SC rupturing capacity of breaker
Equivalent system reactance
Equivalent system reactance at generator bus
= 0.3  0.08 = 0.22 pu
A circuit breaker is employed to quench the magnetizing current of a 80 MVA transformer at 230 kV. The magnetizing current is 4% of full load current. Now, the circuit breaker is opened when the magnetizing current is as its peak value. The stray capacitance is 4 pF and inductance is 25 mH. The maximum voltage appears across the circuit is ______(in kV)
In which case the system of equations
x_{1 }– 2x_{2} + x_{3} = 3
2x_{1} – 5x_{2} + 2x_{3} = 2
x_{1} + 2x_{2} + λx_{3} = μ
has infinite number of solutions?
The system of equations has infinite solutions when ρ(A) = ρ(AB) < n
A system consisting of n components functions if, and only if, at least one of n components functions. Suppose that all the n components of the system function independently, each with probability 3/4. If the probability of functioning of the system is 63./64, then the value of n is
Probability of the component to function (p) = 3/4
Probability of the component not to function (q) = 1/4
Probability of functioning the system = 63/64
⇒ Probability that at least one component function = 63/64
⇒ Probability that no component functions
If a root of the equation 3x^{3} – 4x^{2} – 4x + 7 = 0 is found out using Newton Raphson’s method. If the initial assumption for the root is 2, then the root after two iterations will be – (upto three decimal places)
Evaluate where c is the circle z = 2.
By Cauchy’s integral formula
Let y(x) be the solution of the differential equation
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